Model-theoretic aspects of the Gurarij operator system
- Creators
- Goldbring, Isaac
-
Lupini, Martino
Abstract
We establish some of the basic model theoretic facts about the Gurarij operator system GS recently constructed by the second-named author. In particular, we show: (1) GS is the unique separable 1-exact existentially closed operator system; (2) GS is the unique separable nuclear model of its theory; (3) every embedding of GS into its ultrapower is elementary; (4) GS is the prime model of its theory; and (5) GS does not have quantifier-elimination, whence the theory of operator systems does not have a model companion. We also show that, for any q ∈ N, the theories of M_q -spaces and M_q -systems do have a model companion, namely the Fraïssé limit of the class of finite-dimensional M_q -spaces and M_q -systems respectively; moreover, we show that the model companion is separably categorical. We conclude the paper by showing that no C* algebra can be existentially closed as an operator system.
Additional Information
© Hebrew University of Jerusalem 2018. Received February 26, 2015 and in revised form April 7, 2017. Goldbring's work was partially supported by NSF CAREER grant DMS-1349399. Lupini's work was supported by the York University Susan Mann Dissertation Scholarship and by the ERC Starting grant no. 259527 of Goulnara Arzhantseva. This work was initiated during a visit of the second author to the University of Illinois at Chicago. The hospitality of the UIC Mathematics Department is gratefully acknowledged.Attached Files
Submitted - 1501.04332
Files
| Name | Size | Download all |
|---|---|---|
|
md5:3be3df0246735d263af064bfa7290302
|
295.3 kB | Download |
Additional details
- Eprint ID
- 86361
- DOI
- 10.1007/s11856-018-1691-3
- Resolver ID
- CaltechAUTHORS:20180511-100333585
- NSF
- DMS-1349399
- York University
- European Research Council (ERC)
- 259527
- Created
-
2018-05-14Created from EPrint's datestamp field
- Updated
-
2021-11-15Created from EPrint's last_modified field